C₁₁×#12279 #14589472

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12102
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12279

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	D₈
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₈ ◁ G

344 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,17,21,24)(15,18,22,25)(20,26,27,23)(29,33)(30,36)(31,38)(34,43)(35,42)(37,40)(39,41);(12,14)(13,17)(15,20)(16,21)(18,23)(19,24)(22,27)(25,26)(28,29,32,35)(30,37,39,43)(31,40,38,34)(33,41,42,36);(12,15)(13,18)(14,20)(16,22)(17,23)(19,25)(21,27)(24,26)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5267);